Is it possible to simulate an egg?
Yes, you could use multiple fluid domains with different viscosity settings. The trick is to bake into different folders. 



The UI allows you only to have one fluid domain therefore you need to disable the first one after baking in one folder by setting its type to none. After that you bake the second one and re-enable the first domain.

NOTE: that the domains shouldn't overlap while baking (I'm not sure about that), I tried to reproduce the steps descibed here

The yolks volume was subtracted from the egg-white using a boolean modifier.

The result needs obviously some tweaking: